Related papers: The Einstein equations and multipole moments at nu…
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at…
We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action $S_E \ll \hbar$. This is obtained through a Metropolis algorithm with weight $\exp(-\beta^2 S^2_E)$ and $\beta \gg…
A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional…
This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…
This is a companion article to `Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations' [1]. It clarifies a singular co\"{o}rdinate transformation of an $SO(4)$ invariant metric…
Einstein-Maxwell field equations correspoding to higher dimensional description of static spherically symmetric space-time have been solved under two specific set of conditions, viz., (i) $\rho \ne 0$, $\nu^\prime= 0$ and (ii) $\rho=0$, $…
A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…
In this paper, we first review Huei's formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill…
We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…
We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two…
For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…
We review the vacuum solutions of Einstein's equations in higher dimensions known as Myers-Perry metrics. In many respects, these solutions describing spinning black holes admit the same remarkable properties as the standard Kerr black hole…
A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…
We consider a class of condensed matter theories in a Newtonian framework with a Lagrange formalism related in a natural way with the classical conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i…
The deviation from geodesic motion of the world line of an extended body endowed with multipolar structure up to the mass quadrupole moment is studied in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The properties…
In the present work, we extend and generalize our previous work regarding the scale dependence applied to black holes in the presence of non-linear electrodynamics [1]. The starting point for this study is the Einstein-power-Maxwell theory…
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets…
We give asymptotics for Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null infinity and homogeneous towards time like infinity. We use the asymptotics to show…
Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this…